Impulses-induced p-exponential input-to-state stability for a class of stochastic delayed partial differential equations

This paper proposes a new stability concept called p-exponential input-to-state stability (pISS) for impulsive stochastic delayed partial differential equations (ISDPDEs). By employing the formula for the variation of parameters, the average impulsive interval approach and a new impulsive integral inequality, the sufficient conditions for pISS of ISDPDEs are derived. The issue of impulsive stabilisation to pISS of ISDPDEs is studied. It is unveiled that if the continuous stochastic delay partial differential equations may not be pISS, it can be stabilised by impulsive control. An example is given to illustrate our main results.